U.S. patent number 7,830,998 [Application Number 11/332,395] was granted by the patent office on 2010-11-09 for approximate linear fm synchronization symbols for a bandwidth configurable ofdm modem.
This patent grant is currently assigned to Edgewater Computer Systems, Inc.. Invention is credited to John Fanson.
United States Patent |
7,830,998 |
Fanson |
November 9, 2010 |
Approximate linear FM synchronization symbols for a bandwidth
configurable OFDM modem
Abstract
A communications system permits bandwidth configurability using
a linear frequency modulated (LFM) waveform for
transmitter/receiver synchronization. The system permits
enhancement of MIL-STD-1553 data buses, and is likewise applicable
to any bandwidth-configurable modem.
Inventors: |
Fanson; John (Ottawa,
CA) |
Assignee: |
Edgewater Computer Systems,
Inc. (Kanata, Ontario, CA)
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Family
ID: |
38263137 |
Appl.
No.: |
11/332,395 |
Filed: |
January 17, 2006 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20070165727 A1 |
Jul 19, 2007 |
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Current U.S.
Class: |
375/354; 370/466;
375/227; 375/139 |
Current CPC
Class: |
H04L
27/2602 (20130101); H04L 27/2656 (20130101); H04L
27/2626 (20130101) |
Current International
Class: |
H04L
7/00 (20060101); H04B 1/00 (20060101); H04B
3/46 (20060101); H04J 3/16 (20060101) |
Field of
Search: |
;375/260,139,227,354
;370/466 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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1278323 |
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Jan 2003 |
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EP |
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2004/109475 |
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Dec 2004 |
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WO |
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WO 2005/055543 |
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Jun 2005 |
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WO |
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Primary Examiner: Ghayour; Mohammad H
Assistant Examiner: Hassan; Sarah
Attorney, Agent or Firm: Ogilvy Renault LLP
Claims
What is claimed is:
1. Within a bandwidth configurable modem, a method of generating
synchronization symbols for a transmitted waveform, comprising:
selecting a frequency sub-band for which synchronization symbols
are desired, said sub-band comprising v frequency bins with
associated frequency sub-carriers; and generating synchronization
symbols as a discrete time domain LFM signal x'(n) with signal
values obtained using the equation:
'.function.e.pi..times..times..pi..times..times..times.
##EQU00015## where: N is the length of the signal in samples; n=0
to N-1; and k.sub.0 is the sub-carrier index corresponding to the
first frequency bin within the selected sub-band.
2. The method as claimed in claim 1 further comprising generating
the synchronization symbols directly in the time domain using a
microprocessor to perform one of series expansions and CORDIC
functions.
3. The method as claimed in claim 1 further comprising generating a
time domain look-up table (LUT) with 2N point complex samples,
comprising: using the equation
.function.e.times..pi..times..times..times..times..times.
##EQU00016## to compute the 2N point complex samples to populate
the LUT.
4. The method as claimed in claim 3 further comprising generating a
time domain signal by indexing the LUT using the equation:
.function..function..function..times..times..times..times..times..times..-
times..times..times. ##EQU00017##
5. Within a bandwidth configurable modem, a method of generating
synchronization symbols for a transmitted waveform, comprising:
selecting a frequency sub-band for which synchronization symbols
are desired, said sub-band comprising v frequency bins with
associated frequency sub-carriers; generating synchronization
symbols in a frequency domain using the approximation equation:
'.function..times..times..apprxeq.''.function..times..times..times.e.time-
s..pi..times..times..pi..times. ##EQU00018## where: N is the number
of sub-carrier frequencies for the entire bandwidth; and k.sub.0 is
the index of the sub-carrier corresponding to the first frequency
bin within the selected sub-band; and using an inverse fast Fourier
transform (IFFT) to convert synchronization symbols to a time
domain before the waveform is transmitted.
6. The method as claimed in claim 5 further comprising generating
the synchronization symbols directly in the frequency domain using
a microprocessor to perform one of series expansions and CORDIC
functions.
7. The method as claimed in claim 5 further comprising generating a
frequency domain look-up table (LUT) wherein LUT synchronization
coefficients are represented by 2N evenly spaced complex
coefficients of a unit circle.
8. The method as claimed in claim 7 further comprising generating a
frequency domain signal by mapping LUT synchronization coefficients
to consecutive frequency sub-carriers, using the equation:
'.function..times..times..function..times..times..times..times..times..ti-
mes. ##EQU00019## wherein k.sub.0 represents a first sub-carrier
and v is the number of frequency bins over which the signal is
swept.
9. A bandwidth-configurable modem adapted to generate
synchronization symbols comprising: logic circuits that select a
frequency sub-band for which synchronization symbols are desired,
said sub-band comprising v frequency bins with associated frequency
sub-carriers; and logic circuits that generate synchronization
symbols as a time domain LFM signal x'(n) with signal values
obtained by using the equation:
'.function.e.pi..times..times..pi..times..times..times.
##EQU00020## where: N is the length of the signal in samples; n=0
to N-1; and k.sub.0 is the sub-carrier index corresponding to the
start of the sweep first frequency bin within the selected
sub-band.
10. The bandwidth-configurable modem as claimed in claim 9 wherein
the logic circuits comprise a microprocessor to perform one of
series expansions and CORDIC functions for generating the
synchronization symbols directly in the time domain.
11. The bandwidth-configurable modem as claimed in claim 9 wherein
the logic circuits comprise a time domain look-up table (LUT) with
2N point complex samples populated by using the equation:
.function.e.times..pi..times..times..times. ##EQU00021##
12. The bandwidth-configurable modem as claimed in claim 11 wherein
the logic circuits generate a time domain signal by indexing the
LUT using the equation:
.function..function..function..times..times..times..times..times..times..-
times. ##EQU00022##
13. The bandwidth-configurable modem as claimed in claim 9 further
comprising a bus coupler for interfacing with a MIL-STD-1553 data
bus.
14. A bandwidth-configurable modem adapted to generate
synchronization symbols comprising: logic circuits that select a
frequency sub-band for which synchronization symbols are desired,
said sub-band comprising v frequency bins with associated frequency
sub-carriers; logic circuits that generate synchronization symbols
in a frequency domain using the approximation equation:
'.function..times..times..apprxeq.''.function..times..times..times.e.time-
s..pi..times..times..pi..times. ##EQU00023## where: N is the number
of sub-carrier frequencies for the entire bandwidth; and k.sub.0 is
the index of the sub-carrier corresponding to the first frequency
bin within the selected sub-band; and logic circuits for performing
an inverse fast Fourier transform (IFFT) to convert synchronization
symbols to a time domain before the waveform is transmitted.
15. The bandwidth-configurable modem as claimed in claim 14 wherein
the logic circuits comprise a microprocessor to perform one of
series expansions and CORDIC functions for generating the
synchronization symbols directly in the frequency domain.
16. The method as claimed in claim 14 wherein the logic circuits
comprise a frequency domain look-up table (LUT) adapted to store
LUT synchronization coefficients that are represented by 2N evenly
spaced complex coefficients of a unit circle.
17. The bandwidth-configurable modem as claimed in claim 16 wherein
the logic circuits generate a frequency domain signal by mapping
LUT synchronization coefficients to consecutive frequency
sub-carriers, using the equation:
'.function..times..times..function..times..times..times..times.
##EQU00024## wherein k.sub.0 represents a first sub-carrier and v
is the number of frequency bins over which the signal is swept.
18. The bandwidth-configurable modem as claimed in claim 14 further
comprising a bus coupler for interfacing with a MIL-STD-1553 data
bus.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
This is the first application filed for the present invention.
MICROFICHE APPENDIX
Not Applicable.
TECHNICAL FIELD
The invention relates to orthogonal frequency division multiplexing
(OFDM) based data communications and, in particular, to symbol and
frame synchronization signals for a bandwidth configurable OFDM
modem.
BACKGROUND OF THE INVENTION
MIL-STD-1553b is a 30-year-old standard that defines electrical and
signaling characteristics for communications over avionics buses
used in military and civilian aircraft, as well as in other
applications (ships, trains, shuttles, space stations, etc.). A
Manchester II bi-phase signaling scheme is used over shielded
twisted pair cabling. That signaling scheme does not efficiently
utilize potential bandwidth available on the bus.
OFDM is a communications protocol that may be used to more
optimally utilize the available bandwidth unused by the 1553b
signaling. Of course, bus coupler type, network topology and
filtering of the Manchester II signaling affect how much bandwidth
is available for an "overlay" OFDM communications system.
An OFDM based communications system can be described by transmitter
10 and receiver 30 components shown in FIGS. 1 and 3. The
transmitter 10 includes forward error correction (FEC) 12 applied
to an input data bit stream, followed by a mapping 14 of encoded
bits to frequency domain sub-carriers, which are transformed to a
time domain digital signal by an inverse fast Fourier transform
(IFFT) 16, which is an efficient implementation of an inverse
discrete Fourier transform (IDFT). FEC 12 may be a Reed-Solomon,
convolutional, or any other type of forward error correction
encoding scheme.
Before the digital signal is converted to an analog signal for
transmission to the receiver 30, a preamble, inserted by preamble
insertion 18, includes a number of synchronization symbols 24
(shown in FIG. 2) which are pre-pended to the transmission sequence
to permit synchronization of the transmitted waveform at the
receiver 30, and to facilitate automatic gain control (AGC) and
channel response estimation. A cyclic prefix is usually added to
the OFDM symbols, which are appropriately shaped (windowed and/or
filtered) by symbol shaping 20 before conversion to an analog
signal by an analog front end (AFE) 22. The AFE 22 includes a
digital-to-analog converter (DAC), appropriate analog filtering and
may also include an IF/RF mixing stage to convert the signal to
higher frequencies.
An exemplary OFDM transmission sequence is shown in FIG. 2. As can
be seen, a predetermined number of synchronization symbols 24 are
prepended to data symbols 26.
At the receiver 30, the analog signal is filtered and converted to
a digital signal by an analog-to-digital converter (ADC), not
shown, in a receiver analog front end 32. The appropriate RF/IF
stages are used to convert the received signal to a baseband signal
in a manner well known in the art. An automatic gain control 34
controls input signal level based on power metrics estimated from
the synchronization symbols 24. A fast Fourier transform (FFT)
which is an efficient implementation of the discrete Fourier
transform (DFT) 36 is applied to the sampled signal, with the
timing of the FFT based on detection and timing estimations derived
from the synchronization symbols 24. A channel estimation 46 is
calculated using the synchronization symbols detected by the
synchronization detection unit 44 and is used by the demodulator 38
to remove effects of the channel. This process, called channel
equalization, is performed in the frequency domain. An inverse
mapping function 40 is used to convert demodulated frequency domain
sub-carriers to coded data bits followed by forward error
correction (FEC) decoding 42, which corrects bit errors when
possible and passes the decoded data bits to higher communications
layers.
In addition to using OFDM to utilize unused bandwidth on a 1553b
bus, it has been recognized as desirable to be able to configure
multiple independent networks on the same bus, so that groups of
communications devices can be respectively allocated a certain
proportion of the available spectrum. It would also be useful for
some devices (a host bus controller, for example) to be able to
communicate to devices associated with any of these independent
networks. In order to accomplish these objectives, the
synchronization signaling component of an OFDM-based communications
system must have an efficient implementation and be configurable
"on the fly", as well as having other required properties. These
properties include: a small transmit peak to average power for all
configurations; and cross-correlation properties such that a
receiver configured to operate in one frequency band will not
detect as a valid synchronization signal leakage energy of a
transmitter configured to operate in another frequency band.
Linear FM (LFM) signals are used in communications systems for the
transmission of data as well as for synchronization preambles,
automatic gain control (AGC) and channel response estimation.
Advantages of LFM signals include low peak to average power for
transmission using limited resolution digital to analog converters
and limited linearity amplifiers, and having a narrow correlation
peak for matched filter reception.
OFDM multi-carrier communications schemes, such as HomePlug.RTM.
Version I and AV, often synthesize a LFM signal by storing
frequency domain coefficients in a look up table (LUT) and then
transforming to the time domain using an IDFT. Each LUT coefficient
corresponds to an OFDM sub-carrier and each coefficient has a
non-zero value for sub-carriers ranging over the sweep of the LFM
signal. This system can be configured to sweep over any desired
sub-band by zeroing LUT coefficients corresponding to sub-carriers
outside the sub-band. However this system suffers from the drawback
that when configured for a sub-band, the time domain LFM sweep will
have most of its power concentrated in the time segment
corresponding to the sub-band, significantly increasing the peak to
average power ratio of the signal. For example, if the system is
configured to sweep the first half of the LFM band by zeroing the
upper half of the coefficients, the first half of the LFM waveform
will sweep over this sub-band and the second half will be close to
zero in amplitude. A bandwidth-configurable OFDM modem that
overcomes at least one of these shortcomings would be highly
desirable.
SUMMARY OF THE INVENTION
The instant invention is designed to enhance MIL-STD-1553 data
buses but is likewise applicable to any bandwidth configurable
communications system requiring an LFM waveform to be generated and
therefore not restricted to an OFDM modem. The invention provides a
communications system that permits bandwidth configurability using
a linear frequency modulated (LFM) waveform for
transmitter/receiver synchronization.
In accordance with one aspect of the present invention, a method of
generating LFM synchronization symbols for a bandwidth-configurable
modem includes using the equation
'.function.e.pi..times..times..pi..times..times..times.
##EQU00001## where x'(n) is the discrete time LFM waveform; N is
the length of the waveform in samples; n=0 to N-1; v is the number
of frequency bins over which the signal is swept; and k.sub.0 is
the index of the sub-carrier corresponding to the start of the
sweep.
In accordance with another aspect of the present invention, a
method of generating synchronization symbols for a
bandwidth-configurable modem includes using the approximation
equation
'.function..times..times..apprxeq..times.''.function..times..times..time-
s..times.e.times..pi..times..times..pi..times. ##EQU00002## where:
X'(k) is the DFT of the LFM waveform x'(n); N is the number of
sub-carrier frequencies; k=0 to N-1; v is the number of
sub-carriers over which the signal is swept, and, k.sub.0 is the
index of the sub-carrier corresponding to the start of the sweep;
and using an inverse fast Fourier transform (IFFT) to convert to
the time domain before the waveform is transmitted.
In accordance with yet another aspect of the present invention, a
bandwidth-configurable modem includes logic circuits that generate
the synchronization symbols in a time domain using the equation
'.function.e.pi..times..times..pi..times..times..times.
##EQU00003## where: x'(n) is the discrete time LFM waveform; N is
the length of the waveform in samples; n=0 to N-1; v is the number
of frequency bins over which the signal is swept; and k.sub.0 is
the index of the sub-carrier corresponding to the start of
the-sweep.
In accordance with a further aspect of the present invention, a
bandwidth-configurable modem includes logic circuits that generate
the synchronization symbols in the frequency domain by using the
approximation equation:
'.function..times..times..apprxeq..times.''.function..times..times..time-
s..times.e.times..pi..times..times..pi..times..times. ##EQU00004##
where: X'(k) is the DFT of the LFM waveform x'(n); N is the number
of sub-carrier frequencies; k=0 to N-1; v is the number of
frequency bins over which the signal is swept; and k.sub.0 is the
index of the sub-carrier corresponding to the start of the sweep;
and logic circuits for performing an inverse fast Fourier transform
(IFFT) for converting sub-carrier signals to the time domain before
the waveform is transmitted.
In the above equations, v is understood to be a positive integer
and consequently the equations describe an LFM sweep going from low
to high frequency. However, with minor modifications obvious to one
skilled in the art, the equations can be modified to describe an
LFM sweeping from high to low frequency.
BRIEF DESCRIPTION OF THE DRAWINGS
Further features and advantages of the present invention will
become apparent from the following detailed description, taken in
combination with the appended drawings, in which:
FIG. 1 is a schematic diagram of an exemplary prior art OFDM
transmitter;
FIG. 2 is a schematic diagram of an exemplary prior art OFDM
transmission sequence;
FIG. 3 is a schematic diagram of an exemplary prior-art OFDM
receiver;
FIG. 4 is a graph plotting the normalized magnitude response of
X(k) and of the Discrete Fourier Transform (DFT) of x(n);
FIG. 5 is a graph plotting the phase response of X(k) and of the
Discrete Fourier Transform (DFT) of x(n);
FIG. 6 is a graph plotting the normalized magnitude response of
X''(k) and of the Discrete Fourier Transform (DFT) of x'(n), where
the bandwidth that is swept (v=32) is less than the entire
available bandwidth (N=256) and where k.sub.0=0;
FIG. 7 is a graph plotting the phase response of X''(k) and of the
Discrete Fourier Transform (DFT) of x'(n), where the bandwidth that
is swept (v=32) is less than the entire available bandwidth (N=256)
and where k.sub.0=0;
FIG. 8 is a graph plotting the normalized magnitude response of
X''(k) and of the Discrete Fourier Transform (DFT) of x'(n), where
the bandwidth that is swept (v=32) is less than the entire
available bandwidth (N=256) and where k.sub.0=32;
FIG. 9 is a graph plotting the phase response of X''(k) and of the
Discrete Fourier Transform (DFT) of x'(n), where the bandwidth that
is swept (v=32) is less than the entire available bandwidth (N=256)
and where k.sub.0=32;
FIG. 10 depicts the use of a single LUT to generate the LFM
synchronization symbols;
FIG. 11 depicts, in a complex plane, a unit circle from which 2N
evenly spaced complex coefficients are derived to represent synch
coefficients in a LUT;
FIG. 12 is a time-domain representation of a approximated and exact
synchronization symbol for N=256, v=64 and k.sub.0=0;
FIG. 13 is a time-domain representation of the approximated and
exact LFM signals for N=256, v=64 and k0=0; and
FIG. 14 is a schematic diagram of a bandwidth-configurable modem in
accordance with the invention.
It will be noted that throughout the appended drawings, like
features are identified by like reference numerals.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Linear FM Synchronization Symbols
It can be demonstrated that for the following complex sampled LFM
signal (quadratic phase modulation),
.function.e.times..pi..times..times..times. ##EQU00005## the
discrete Fourier transform (DFT) defined by
.function..times..function..times.e.pi..times..times..times..times..times-
..times..times. ##EQU00006## is given by
.function..times.e.times..pi..times..times..pi..times..times..times..time-
s..times. ##EQU00007## where: n=0 to N-1 and k=0 to N-1.
This implies that the DFT of this particular LFM signal results in
an equivalent LFM signal except for a scaling of {square root over
(N)} and a .pi./4 phase shift. The functional form of the signal is
the same in the time and frequency domains.
This can be seen in the magnitude and phase responses of the DFT of
x(n) and X(k) as shown in FIGS. 4 and 5, for N=64 (the magnitudes
were normalized to 1 for the purpose of illustration).
It should be noted that the phase of the signals extends beyond
-.pi. and .pi. allowing one to see the quadratic nature of the
curve.
x(n) is a specific case (v=N, k.sub.0=0) of the more general LFM
function,
'.function.e.pi..times..times..times..times..pi..times..times..times..tim-
es..times. ##EQU00008## where v can be considered the number of
frequency bins over which the signal is swept, and k.sub.0 the
index of the sub-carrier corresponding to the start of the LFM
sweep. For v=N, the DFT of x'(n) is X'(k)=X(k-k.sub.0).sub.mod N
Equation 5 where the spectrum of X(k) is circularly shifted by
k.sub.0 frequency bins.
Unfortunately, for v equal to anything other than N, the quadratic
phase modulation represented by Equation 3 in the frequency domain
no longer applies. It can, however, be shown to be a reasonable
approximation, especially for an efficient generation of
synchronization signals for OFDM based communications systems
applications.
With the appropriate scaling, the DFT of x'(n) is approximated
by
'.function..times..times..apprxeq..times.''.function..times..times..time-
s..times.e.times..pi..times..times..pi..times..times..times.
##EQU00009## for v.noteq.n.
FIGS. 6 and 7 illustrate the effect of limiting the bandwidth that
is swept (v) to less than the entire bandwidth (N) for Equation 6.
In this case, N=256, v=32 and k.sub.0=0. FIGS. 8 and 9 show the
effect of limiting the width of the LFM sweep to v=32 and offseting
the start of the sweep by k.sub.0=32.
Note that the coefficients are just rotated which hints at an
efficient implementation.
The phase response of Equation 6 is a much better approximation to
the phase response of the DFT of x'(n) than the corresponding
magnitude responses.
The synchronization symbols for an OFDM preamble can be generated
in the time domain or the frequency domain. In either case, it is
desirable to use quadratic phase modulation (in time or across
frequency) to generate the symbols using the formula of either
Equation 4 or Equation 6, respectively. If the quadratic phase
modulated symbol is generated in the frequency domain, an IFFT is
used to convert the signal to the time domain before it is
transmitted. If the LFM synchronization symbols are generated
directly in the time domain using Equation 4, this results in a
power spectral density that is not constant. If the synchronization
symbols are generated in the frequency domain using Equation 6, the
power spectral density is constant across the swept band. For an
OFDM based communications system, it is desirable to have a
constant power spectral density across the swept frequency
band.
Look-Up-Table (LUT) Implementation
In accordance with one embodiment of the invention, a very
efficient method of using a look-up table is provided for
configuring any frequency band with appropriate coefficients based
on the LFM approximation of Equation 6 for an appropriate selection
of configurable bandwidths. Note that in equation 6 the angle
argument is always an integer multiple of .pi./N providing that v
divides evenly into N. Consequently a 2N value look up table (LUT)
can be constructed to precisely generate the frequency domain LFM
values of equation 6, as shown in FIG. 10. In this example, a
synchronization coefficient LUT 50 has a table index of 0 to 15
(i.e. 2N=16, N=8), which provides circular modulo (2N) indexing for
the LUT. An IFFT buffer 52 temporarily stores the LUT coefficients
for inverse FFT processing by an IFFT filter 54, which generates a
LFM time series x(n) 56. In this example, it is assumed that N=8,
k.sub.0=2 and v=4. Once computed, the step size through the table
is translated to a LUT table index of [0 2 8 2] (as per Equation 7,
below) where the last index value (2) is the result of 18 modulo
16.
The synchronization coefficient look-up table (LUT) represents 2N
evenly spaced complex coefficients of the unit circle 60 as shown
in FIG. 11. Note that any constant phase rotation of the
coefficients is un-important. Also, because of the symmetry of the
coefficients in the complex plane 62, the number of LUT elements
could be reduced at the expense of some additional logic. Quadratic
phase modulation is obtained by stepping through the LUT
coefficients in a quadratic way (modulus 2N for a circular table)
and mapping them to consecutive frequency sub-carriers with the
first sub-carrier being k.sub.0 as defined in Equation 7.
'.function..times..times..function..times..times..times..times..times..ti-
mes..times..times. ##EQU00010##
The time series, such as the one shown in FIG. 12, can be generated
by an IFFT. The time series can be made complex (in phase and
quadrature) with the appropriate FFT architecture or real,
depending on the type of signaling required. FIG. 12 illustrates
the time domain representation of a synchronization symbol for
N=256, v=64 taking a real part of the IFFT output. The exact LFM
signal is included for comparison. It should be noted that in this
case every N/v sample is equivalent.
Using a configurable bandwidth specified by a value of v that
divides evenly into N results in precise quadratic phase modulation
across frequency sub-carriers in all cases.
In practice, if N is large enough, the configurable bandwidth can
be specified by a value of v that does not divide evenly into N. In
this case the LUT index value calculated by equation 7 may be non
integer and the LUT value can be determined by some interpolation
technique (including nearest neighbor interpolation which amounts
to rounding LUT index) . Reductions in LUT size can be obtained
using methods like CORDIC approximations for sine and cosine
functions. As is known in the art, CORDIC (COordinate Rotation
DIgital Computer) functions constitute a simple and efficient
algorithm to calculate hyperbolic and trigonometric functions.
Other Implementations
Time Domain
'.function.e.pi..times..times..pi..times..times..times..times..times.
##EQU00011## can be employed to generate the synchronization
symbols directly in the time domain using a microprocessor (CPU,
ALU, floating point co-processor . . . ) and known methods (series
expansions, look-up table, CORDIC functions, etc.). For a
bandwidth-configurable system, the parameters are modified for the
different bandwidths (v) and starting frequencies (k.sub.0). This
results in a power spectral density that is not constant (but can
be flattened with appropriate windowing and filtering). For a
system where latency when switching configurations is an issue,
i.e. bandwidth configurable "on the fly", having better control
over the power spectral density and having an ability to turn off
sub-carriers that may be interfering with sensitive equipment or
violating emissions limits as set by MIL-STD-461e and FCC part 15,
there are more suitable ways to generate synchronization symbols.
Efficient Look-Up Table Implementation
In accordance with one embodiment of the invention, an efficient
LUT implementation for generating synchronization symbols in the
time domain is possible when the limitations described above are
not an issue. A time domain LUT with 2N point complex samples is
generated using the formula:
.function.e.times..pi..times..times..times..times..times..times..times.
##EQU00012##
The time domain signal can be generated by indexing the LUT
according to the following equation:
.function..function..function..times..times..times..times..times..times..-
times..times..times..times..times..times. ##EQU00013## which
combines linear indexing through the table to generate the carrier
frequency with quadratic indexing through the table to generate the
linear frequency modulation.
The rounding function is required because there are not enough
coefficients to precisely describe the LFM modulation in the time
domain. Instead of the rounding to obtain an integer LUT index, the
LUT can be interpolated. In any case, the approximation is suitable
for most applications and the LUT can be further reduced if
accuracy requirements permit it. FIG. 13 illustrates the
approximate LFM signal generated in the time domain using this
method for N=256, v=64, taking the real part. The exact LFM signal
is included for comparison.
Frequency Domain
Directly
.function..times..times.e.times..pi..times..times..times.
##EQU00014## (for k=0 to v-1, X(k)=0 otherwise, ignoring .pi./4
phase rotation) can be employed to generate the synchronization
symbols using a microprocessor (CPU, ALU, floating point
co-processor, etc.) directly in the frequency domain using known
methods (series expansions, LUT, CORDIC functions, etc.). For a
bandwidth configurable system, the parameters are modified for the
different bandwidths (v) and starting frequencies (k.sub.0). The
time domain signal is generated using an IFFT.
FIG. 14 is a block diagram of a bandwidth-configurable OFDM modem
100 having logic circuits for generating synchronization symbols in
accordance with embodiments of the invention. All of the components
of the modem 100 are identical to those described above with
reference to FIGS. 1 and 3 and their descriptions will not be
repeated for that reason. In addition, the modem 100, or a
microprocessor 106 associated with the modem 100, is provisioned
with algorithms for performing series expansions and/or Coordinate
Rotational Digital Computer (CORDIC) functions 102, and/or a
look-up table 104 for generating synchronization symbols using the
method in accordance with the invention, as described above in
detail. The microprocessor 106 may be an integral part of the modem
100 or part of an auxiliary unit. The bandwidth used by the modem
100 may be statically configured using hardware or software control
parameters in a manner known in the art. The bandwidth used by the
modem may also be configured "on the fly" by downloading values for
N and v via a modem control channel (not shown). The analog front
end 22 of the transmitter and the analog front end 32 of the
receiver are, in accordance with one embodiment of the invention,
interfaced with a MIL-STD-1553 data bus via bus couplers 110, 112,
respectively.
The main benefit is that the LFM synchronization signal will be
swept only over the configured bandwidth for the duration of the
symbol. This results in a peak to average power that is constant
and independent of the configured bandwidth. This also permits the
inclusion of a sub-carrier mask to turn off selected tones in the
configured bandwidth as required.
In the foregoing description of the invention, the variable "v" in
the equations is understood to be a positive integer. Consequently,
the equations describe an LFM that sweeps from a low frequency to a
high frequency. However, with minor modifications obvious to one
skilled in the art, those equations can be modified to describe an
LFM that sweeps from a high frequency to a low frequency.
The embodiment(s) of the invention described above is (are)
intended to be exemplary only. The scope of the invention-is
therefore intended to be limited solely by the scope of the
appended claims.
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